1. Marr’s Three Levels Presented by Allen Houng

2. Contents • General Introduction • The Philosophy and the Approach • Background • Understanding Complex Information-processingsystems • Representation and description • Process • The three levels • Importance of computational theory • The approach of J.J. Gibson • A Representational Framework for Vision • The purpose of vision • Advanced vision • To the desirable via the possible

3. General Introduction • Vision is an information-processing task: Representation Processes (computations) • Multi-level explanation is required. perspective of the plain men perspective of experimental psychologist perspective of programming

4. The philosophy and the approachBackground • 1950s and 1960s: many important discoveries in many different fields. • AI, neuroscience, psychophysics, … • But nothing similar happened after 1970s. No neurophysiologists had recorded new and clear high-level correlates of perception. The leaders of 60s have turned away from what they had been doing – Hubel and Wiesel focused on anatomy, Barlow turn to psychophysics, …

5. Neurophysiologists: similar situation • Gross’s hand-detectors tell us that they exist, but not why and how they do. • Single-unit recording tells us nothing about how to program them on a computer. • Neurophysiology and psychophysics can describe the behavior of cells or of subjects but not to explain such behavior.

6. Questions left out • What are the visual area of the cerebral cortex actually doing? • What are the problems in doing it that need explaining? • At what level of description should such explanation sought?

7. The failure of AI • Ad hoc program of computer vision • Restricted, mini visual world • Explanation in terms of neurons

8. Marr’s core idea • “There must exist an additional level of understanding at which the character of the information-processing tasks carried out during perception are analyzed and understood in a way that is independent of the particular mechanisms and structures that implement them in our head. This was what was missing – the analysis of the problem as an information-processing task. Such analysis does not usurp an understanding at the other levels, of neurons or of computer programs – but is a necessary complement to them, since without it there can be no real understanding of the function of all those neurons.”

9. Representation and description • Representation = a formal system for making explicit certain entities or types of information, together with a specification of how the system does this. • Description = the result of using representations

10. Process • The transformation, interaction, connection, manipulation of representations • Two components: representation and algorithm

11. The three levels What is the goal of the computation? Why is it appropriate? What is the logic of the strategy by which it can be carried out? • Computational theory • Representation and algorithm • Hardware implementation How can this computational theory be implemented? In particular, what is the representation for the input and output,? What is the algorithm for the transformation? How can the representation and algorithm be realized physically?

12. Importance of computational theory • An algorithm is likely to be understood more readily by understanding the nature of the computational problem being solved than by examining the mechanism (and the hardware) in which it is embodied. • To understand perception by studying only neurons is like trying to understand bird flight by studying only feathers.

13. The approach of J. J. Gibson • Direct pickup of invariant properties in the ambient light array • Do not assume representation and process • Marr’s criticisms: • The detection of physical invariants is exactly and precisely and information-processing problem • Gibson vastly underrated the sheer difficulty of such detection

14. A representational framework for vision Name Purpose Primitives Image Represents intensity Intensity value at each point in the image Primal sketch Makes explicit important information about the two-dimensional image, primarily the intensity changes there and their geometrical distribution and organization. Zero-crossings Blobs Terminations and discontinuities Edge segments Virtual lines Groups Curvilinear organization Boundaries

15. A representational framework for vision Name Purpose Primitives Image Represents intensity Intensity value at each point in the image Primal sketch Makes explicit important information about the two-dimensional image… Zero-crossings 21/2-D sketch Make explicit the orientation and rough depth of the visible surfaces, and contours of discontinuities in these quantities in a viewer-centered coordinate frame. Local surface orientation (the “needles” primitives) Distance from view Discontinuities in depth Discontinuities in surface orientation

16. A representational framework for vision Name Purpose Primitives Image Represents intensity Intensity value at each point in the image Makes explicit important information about the two-dimensional image… Primal sketch Zero-crossings 21/2-D sketch Make explicit the orientation and rough depth of the visible surfaces Local surface orientation (the “needles” primitives) 3-D model Describes shapes and their spatial organization in an object-centered coordinate frame, using a modular hierarchical representation that includes volumetric primitives (i.e., primitives that represent the volume of space that a shape occupies) as well as surface primitives. 3-D models arranged hierarchically, each one based on a spatial configuration of a few sticks or axes, to which volumetric or surface shape primitive are attached

17. A sequence of representations are necessary. • Starting with images on retina, we gradually reach a more objective, physical properties about an object’s shape. • From 2-d images to viewer-centered surface description to object-centered object description

18. Criticisms of Marr • Two senses of the notion of level: • Levels of description, levels of theories, levels of analysis, epistemic levels • Levels of existence, levels of organization, ontological levels

19. Marr’s notion of level is theoretical rather than ontological. • Marr says, “three levels of description … are logically and causally related.” (p. 248) • For the notion of theoretical levels, levels are only logically related, not causally related. Marr confuses ontological level with epistemic level.

20. Triple-level model • Marr is quite right in proposing triple-level model of visual perception. • Any adequate model of anything must be a triple-level model.

21. THE END